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MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

israelhayom.com

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Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#11

Post by apple314159 »

nthcolumn wrote: post #8
jschulenklopper wrote: post #3

From the article: > According to the new "Three Radii Theorem," if three or more lines extend from a single point to the edge of a circle, then the point is the center of the circle and the straight lines are the radii. Shouldn't that be "three or more lines of equal length ", and "to different points on the edge of a circle"? Or am I missing something?

And wouldn't two of equal length do? I think we are missing an explanation of the theorem. edit: oh hang on, I see now: Trump Foundation It's one of those theorems. edit: yes three mean they can't be longer than the radius. Isn't it interesting. You need 3 for a circle. What about other shapes?

With only two lines of equal distance. the point may not be in the center.

Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#12

Post by [deleted] »

hydroo wrote: post #7
jschulenklopper wrote: post #3

From the article: > According to the new "Three Radii Theorem," if three or more lines extend from a single point to the edge of a circle, then the point is the center of the circle and the straight lines are the radii. Shouldn't that be "three or more lines of equal length ", and "to different points on the edge of a circle"? Or am I missing something?

The theorem as stated in the article is definitely wrong. Equal length would make it correct, I think.

[deleted]

Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#13

Post by ronnybrendel »

jschulenklopper wrote: post #3

From the article: > According to the new "Three Radii Theorem," if three or more lines extend from a single point to the edge of a circle, then the point is the center of the circle and the straight lines are the radii. Shouldn't that be "three or more lines of equal length ", and "to different points on the edge of a circle"? Or am I missing something?

The theorem as stated in the article is definitely wrong. Equal length would make it correct, I think.

Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#14

Post by jschulenklopper »

nthcolumn wrote: post #8
jschulenklopper wrote: post #3

From the article: > According to the new "Three Radii Theorem," if three or more lines extend from a single point to the edge of a circle, then the point is the center of the circle and the straight lines are the radii. Shouldn't that be "three or more lines of equal length ", and "to different points on the edge of a circle"? Or am I missing something?

And wouldn't two of equal length do? I think we are missing an explanation of the theorem. edit: oh hang on, I see now: Trump Foundation It's one of those theorems. edit: yes three mean they can't be longer than the radius. Isn't it interesting. You need 3 for a circle. What about other shapes?

Imagine a point inside a circle, close to the edge, and draw two lines to different points to the edge. That point isn't necessarily the center.

Unless you add a third line of equal distance that needs to go to yet another point on the edge. The only way to make that work is if the point is in the center (and the lines automatically are radii).

Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#15

Post by [deleted] »

nthcolumn wrote: post #8
jschulenklopper wrote: post #3

From the article: > According to the new "Three Radii Theorem," if three or more lines extend from a single point to the edge of a circle, then the point is the center of the circle and the straight lines are the radii. Shouldn't that be "three or more lines of equal length ", and "to different points on the edge of a circle"? Or am I missing something?

And wouldn't two of equal length do? I think we are missing an explanation of the theorem. edit: oh hang on, I see now: Trump Foundation It's one of those theorems. edit: yes three mean they can't be longer than the radius. Isn't it interesting. You need 3 for a circle. What about other shapes?

[deleted]

Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#16

Post by [deleted] »

hydroo wrote: post #7
jschulenklopper wrote: post #3

From the article: > According to the new "Three Radii Theorem," if three or more lines extend from a single point to the edge of a circle, then the point is the center of the circle and the straight lines are the radii. Shouldn't that be "three or more lines of equal length ", and "to different points on the edge of a circle"? Or am I missing something?

The theorem as stated in the article is definitely wrong. Equal length would make it correct, I think.

[deleted]

Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#17

Post by catpolice »

eximius wrote: post #2

Hm, a clever little theorem. I'm surprised it isn't recorded somewhere. Perhaps it's just under a different name because of it's relative... simplicity? Not to belittle her accomplishment. This is something you'd expect Euclid to write about or something.

It follows from the statement that if two circles intersect in more than two points, they're identical. Which seems like a familiar theorem, that I can't seem to place. So it's more like a corollary. It would be remarkable if this hadn't come up before, but I want to believe because of how good a story it makes...

Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#18

Post by sobbybutter »

hydroo wrote: post #7
jschulenklopper wrote: post #3

From the article: > According to the new "Three Radii Theorem," if three or more lines extend from a single point to the edge of a circle, then the point is the center of the circle and the straight lines are the radii. Shouldn't that be "three or more lines of equal length ", and "to different points on the edge of a circle"? Or am I missing something?

The theorem as stated in the article is definitely wrong. Equal length would make it correct, I think.

Nope, you can have two equal lines extending from a non-central point. Connecting the points would give you an isosceles triangle.

Re: MIT Mathematician confirms: Israeli 10th-grader discovers new geometric theorem

#20

Post by PhantomGremlin »

I loved the brief summary at the top.

In contrast, many times there are "long form" articles which expect me to invest 10 minutes reading them before I even have a good idea what they're about. You know what I mean: Someone grew up privileged, or in the 'hood. Then had a plethora of tangential life experiences. Then maybe an epiphany. Then we begin to read something about the purported topic.

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